4.2 (Uncertainty, 25 Points) Emily has bought a new car. She is not a good driver and likely to have an accident. She reckons that the probability that she will have an accident in 2021 is 25%. If undamaged, the car will have a value of 10,000 next year, but the value of the car decreases by 4,400 in case of an accident. Additionally she has 4,400 in cash. Her utility over wealth is given by 15(3) 2 . (a) Write down the lottery, compute the expected value, and compute Emily's expected utility. [5] (b) Compute the certainty equivalent of not being insured. Compare to the expected value computed in (a). Which one is larger? Why is this the case? [5] (c) Now suppose an insurance company offers her, For an unconditional payment of 1200, to cover the full cost of a damage caused by an accident. Will she buy this insurance (i1c it is the only one available)? What is the highest price she would be willing to pay for this insurance? [7] (d) Now suppose the insurance company offers another contract with a copay of 400 at a price of 1000, i.e. the insurance only pays 4000 in case of an accident. Will Emily buy this insurance (if it is the only one available)? What would be the maximal sum a risk neutral decision maker is willing to pay for an insurance with 400 copay? Discuss. [7] (a) For Emily , the lottery is an accident with 25%% probability. Expected value is EV = 0.75 (10000 + 4400) + 0.25 (10000+4400 -4400) = 0.75 x 14400 + 0.25 x 10000 = 10 800 + 2500 = 13300 Expected utility is EU = 0.75 N10000 + 4400 + 0.25 10000 +4400- 4400 = 0. 75 14 400 + 0.2510 000 = 0.75 . 120 + 0.25. 100 = 0+ 25 = 115 ( b). Certainty equivalent is a guaranted return that she would accept now. Given the EU = 115 , and the utility junction is u= N3 115 =NCE CE = 13225